New approach to diffraction problems solution by reducing it to Volterra integral equation

Abstract

A new approach to solving diffraction problems is proposed. It is based on combining integral equation for the electromagnetic field inside the diffracting object with an integral expression, which determines the diffracted field in the external region after the field inside it. It allows one to obtain the Volterra integral equation with a free term containing the diffracted and incident fields, which can be solved by convergent iterations, giving as a result an expression for the field inside the object, determined after the external one. This expression enables one to obtain an equation connecting the external field and the object parameters, with lower dimension than the initial one. For the presented example as a 1D problem, this equation is just an algebraic one, which allows the solution of the direct problem as well as the inverse one.